The given statements are:

1. A is older than B.
2. C and D are of the same age.
3. E is the youngest.
4. F is younger than D.
5. F is older than A.

So, the persons we need to consider are: A, B, C, D, E, and F, i.e. 6 in total.

We must use statements 2 and 3, as C has been mentioned only in statement 2, and E has been mentioned only in statement 3. Now, we need to account for A, B, D and F. We can account for A and B using statement 1, and for D and F using statement 4.

Using statements 1 and 3, we get: $A > B > E$ Using statements 2 and 4, we get: $C = D > F$

However, we still need statement 5 to find out the relative ages of these two groups. Using statement 5, we get: $C = D > F > A > B > E$

So, C and D are the oldest and to find this out we need to use all the given five statements.

Hence, option (D) is correct.